A student sees a palindrome in the date 01 02 2010, and wonders how to
generate all such palindromic dates. Building on another math doctor's
work with date arithmetic, Doctor Carter shares a program written in C,
then goes on to explain the purpose of each line of code.

I need to know how to get positive integer solutions of two
Diophantine equations having three variables. For example: 2x + 3y +
7z = 32 ; 3x + 4y - z = 19. (Give the positive set of triples for the
above equations.)

A student of mine noticed that in every Pythagorean triple, a or b is
divisible by 3, a or b is divisible by 4, and a, b, or c is divisible
by 5 (sometimes the same number meets more than one of the
conditions). We are trying to determine if this is really true, and
if so, how to prove it.